Related papers: On the concept of complexity in random dynamical s…
To quantify the fundamental evolution of time-varying networks, and detect abnormal behavior, one needs a notion of temporal difference that captures significant organizational changes between two successive instants. In this work, we…
This paper introduces a comprehensive framework for complex-valued probability measures and explores their novel applications in information theory and statistical analysis. We define a complex probability measure as a phase-modulated…
Information theory on a time-discrete setting in the framework of time series analysis is generalized to the time-continuous case. Considerations of the Roessler and Lorenz dynamics as well as the Ornstein-Uhlenbeck process yield for…
A simple model of an irreversible process is introduced. The equation of iterations in the model includes a noise generation term. We study the properties of the system when the noise generation term is a stochastic process (e.g. a random…
Nonlinear dynamical systems are ubiquitous in nature and they are hard to forecast. Not only they may be sensitive to small perturbations in their initial conditions, but they are often composed of processes acting at multiple scales.…
What is the relationship between the complexity of a learner and the randomness of his mistakes? This question was posed in \cite{rat0903} who showed that the more complex the learner the higher the possibility that his mistakes deviate…
In this work, several random Boolean networks (RBN) are generated and analyzed from two characteristics: their time evolution diagram and their transition diagram. For this purpose, its randomness is estimated using three measures, of which…
We evaluate new complexity measures on the symbolic dynamics of coupled tent maps and cellular automata. These measures quantify complexity in terms of $k$-th order statistical dependencies that cannot be reduced to interactions between…
Symbolic dynamics has proven to be an invaluable tool in analyzing the mechanisms that lead to unpredictability and random behavior in nonlinear dynamical systems. Surprisingly, a discrete partition of continuous state space can produce a…
Data complexity is an important concept in the natural sciences and related areas, but lacks a rigorous and computable definition. In this paper, we focus on a particular sense of complexity that is high if the data is structured in a way…
Algorithms increasingly operate within complex physical, social, and engineering systems where they are exposed to disturbances, noise, and interconnections with other dynamical systems. This article extends known convergence guarantees of…
We show that, when music pieces are cast in the form of time series of pitch variations, the concepts and tools of dynamical systems theory can be applied to the analysis of {\it temporal dynamics} in music. (i) Phase space portraits are…
We consider the concept of statistical complexity to write the quasiperiodical damped systems applying the snapshot attractors. This allows us to understand the behaviour of these dynamical systems by the probability distribution of the…
The exact computation of orbits of discrete dynamical systems on the interval is considered. Therefore, a multiple-precision floating point approach based on error analysis is chosen and a general algorithm is presented. The correctness of…
The intuition that a long history is required for the emergence of complexity in natural systems is formalized using the notion of depth. The depth of a system is defined in terms of the number of parallel computational steps needed to…
We study systems with periodically oscillating parameters that can give way to complex periodic or non periodic orbits. Performing the long time limit, we can define ergodic averages such as Lyapunov exponents, where a negative maximal…
In experiments, the dynamical behavior of systems is reflected in time series. Due to the finiteness of the observational data set it is not possible to reconstruct the invariant measure up to arbitrary fine resolution and arbitrary high…
We present some new results which relate information to chaotic dynamics. In our approach the quantity of information is measured by the Algorithmic Information Content (Kolmogorov complexity) or by a sort of computable version of it…
A practical measure for the complexity of sequences of symbols (``strings'') is introduced that is rooted in automata theory but avoids the problems of Kolmogorov-Chaitin complexity. This physical complexity can be estimated for ensembles…
A quantum trajectory describes the evolution of a quantum system undergoing indirect measurement. In the discrete-time setting, the state of the system is updated by applying Kraus operators according to the measurement results. From an…